--- /dev/null
+(* Copyright (C) 2000, HELM Team.
+ *
+ * This file is part of HELM, an Hypertextual, Electronic
+ * Library of Mathematics, developed at the Computer Science
+ * Department, University of Bologna, Italy.
+ *
+ * HELM is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU General Public License
+ * as published by the Free Software Foundation; either version 2
+ * of the License, or (at your option) any later version.
+ *
+ * HELM is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with HELM; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+ * MA 02111-1307, USA.
+ *
+ * For details, see the HELM World-Wide-Web page,
+ * http://cs.unibo.it/helm/.
+ *)
+
+(* $Id$ *)
+
+exception CannotSubstInMeta;;
+exception RelToHiddenHypothesis;;
+exception ReferenceToVariable;;
+exception ReferenceToConstant;;
+exception ReferenceToCurrentProof;;
+exception ReferenceToInductiveDefinition;;
+
+let debug_print = fun _ -> ()
+
+let lift_from k n =
+ let rec liftaux k =
+ let module C = Cic in
+ function
+ C.Rel m ->
+ if m < k then
+ C.Rel m
+ else
+ C.Rel (m + n)
+ | C.Var (uri,exp_named_subst) ->
+ let exp_named_subst' =
+ List.map (function (uri,t) -> (uri,liftaux k t)) exp_named_subst
+ in
+ C.Var (uri,exp_named_subst')
+ | C.Meta (i,l) ->
+ let l' =
+ List.map
+ (function
+ None -> None
+ | Some t -> Some (liftaux k t)
+ ) l
+ in
+ C.Meta(i,l')
+ | C.Sort _ as t -> t
+ | C.Implicit _ as t -> t
+ | C.Cast (te,ty) -> C.Cast (liftaux k te, liftaux k ty)
+ | C.Prod (n,s,t) -> C.Prod (n, liftaux k s, liftaux (k+1) t)
+ | C.Lambda (n,s,t) -> C.Lambda (n, liftaux k s, liftaux (k+1) t)
+ | C.LetIn (n,s,ty,t) ->
+ C.LetIn (n, liftaux k s, liftaux k ty, liftaux (k+1) t)
+ | C.Appl l -> C.Appl (List.map (liftaux k) l)
+ | C.Const (uri,exp_named_subst) ->
+ let exp_named_subst' =
+ List.map (function (uri,t) -> (uri,liftaux k t)) exp_named_subst
+ in
+ C.Const (uri,exp_named_subst')
+ | C.MutInd (uri,tyno,exp_named_subst) ->
+ let exp_named_subst' =
+ List.map (function (uri,t) -> (uri,liftaux k t)) exp_named_subst
+ in
+ C.MutInd (uri,tyno,exp_named_subst')
+ | C.MutConstruct (uri,tyno,consno,exp_named_subst) ->
+ let exp_named_subst' =
+ List.map (function (uri,t) -> (uri,liftaux k t)) exp_named_subst
+ in
+ C.MutConstruct (uri,tyno,consno,exp_named_subst')
+ | C.MutCase (sp,i,outty,t,pl) ->
+ C.MutCase (sp, i, liftaux k outty, liftaux k t,
+ List.map (liftaux k) pl)
+ | C.Fix (i, fl) ->
+ let len = List.length fl in
+ let liftedfl =
+ List.map
+ (fun (name, i, ty, bo) -> (name, i, liftaux k ty, liftaux (k+len) bo))
+ fl
+ in
+ C.Fix (i, liftedfl)
+ | C.CoFix (i, fl) ->
+ let len = List.length fl in
+ let liftedfl =
+ List.map
+ (fun (name, ty, bo) -> (name, liftaux k ty, liftaux (k+len) bo))
+ fl
+ in
+ C.CoFix (i, liftedfl)
+ in
+ liftaux k
+
+let lift n t =
+ if n = 0 then
+ t
+ else
+ lift_from 1 n t
+;;
+
+(* subst t1 t2 *)
+(* substitutes [t1] for [Rel 1] in [t2] *)
+(* if avoid_beta_redexes is true (default: false) no new beta redexes *)
+(* are generated. WARNING: the substitution can diverge when t2 is not *)
+(* well typed and avoid_beta_redexes is true. *)
+let rec subst ?(avoid_beta_redexes=false) arg =
+ let rec substaux k =
+ let module C = Cic in
+ function
+ C.Rel n as t ->
+ (match n with
+ n when n = k -> lift (k - 1) arg
+ | n when n < k -> t
+ | _ -> C.Rel (n - 1)
+ )
+ | C.Var (uri,exp_named_subst) ->
+ let exp_named_subst' =
+ List.map (function (uri,t) -> (uri,substaux k t)) exp_named_subst
+ in
+ C.Var (uri,exp_named_subst')
+ | C.Meta (i, l) ->
+ let l' =
+ List.map
+ (function
+ None -> None
+ | Some t -> Some (substaux k t)
+ ) l
+ in
+ C.Meta(i,l')
+ | C.Sort _ as t -> t
+ | C.Implicit _ as t -> t
+ | C.Cast (te,ty) -> C.Cast (substaux k te, substaux k ty)
+ | C.Prod (n,s,t) -> C.Prod (n, substaux k s, substaux (k + 1) t)
+ | C.Lambda (n,s,t) -> C.Lambda (n, substaux k s, substaux (k + 1) t)
+ | C.LetIn (n,s,ty,t) ->
+ C.LetIn (n, substaux k s, substaux k ty, substaux (k + 1) t)
+ | C.Appl (he::tl) ->
+ (* Invariant: no Appl applied to another Appl *)
+ let tl' = List.map (substaux k) tl in
+ begin
+ match substaux k he with
+ C.Appl l -> C.Appl (l@tl')
+ (* Experimental *)
+ | C.Lambda (_,_,bo) when avoid_beta_redexes ->
+ (match tl' with
+ [] -> assert false
+ | [he] -> subst ~avoid_beta_redexes he bo
+ | he::tl -> C.Appl (subst he bo::tl))
+ | _ as he' -> C.Appl (he'::tl')
+ end
+ | C.Appl _ -> assert false
+ | C.Const (uri,exp_named_subst) ->
+ let exp_named_subst' =
+ List.map (function (uri,t) -> (uri,substaux k t)) exp_named_subst
+ in
+ C.Const (uri,exp_named_subst')
+ | C.MutInd (uri,typeno,exp_named_subst) ->
+ let exp_named_subst' =
+ List.map (function (uri,t) -> (uri,substaux k t)) exp_named_subst
+ in
+ C.MutInd (uri,typeno,exp_named_subst')
+ | C.MutConstruct (uri,typeno,consno,exp_named_subst) ->
+ let exp_named_subst' =
+ List.map (function (uri,t) -> (uri,substaux k t)) exp_named_subst
+ in
+ C.MutConstruct (uri,typeno,consno,exp_named_subst')
+ | C.MutCase (sp,i,outt,t,pl) ->
+ C.MutCase (sp,i,substaux k outt, substaux k t,
+ List.map (substaux k) pl)
+ | C.Fix (i,fl) ->
+ let len = List.length fl in
+ let substitutedfl =
+ List.map
+ (fun (name,i,ty,bo) -> (name, i, substaux k ty, substaux (k+len) bo))
+ fl
+ in
+ C.Fix (i, substitutedfl)
+ | C.CoFix (i,fl) ->
+ let len = List.length fl in
+ let substitutedfl =
+ List.map
+ (fun (name,ty,bo) -> (name, substaux k ty, substaux (k+len) bo))
+ fl
+ in
+ C.CoFix (i, substitutedfl)
+ in
+ substaux 1
+;;
+
+(*CSC: i controlli di tipo debbono essere svolti da destra a *)
+(*CSC: sinistra: i{B/A;b/a} ==> a{B/A;b/a} ==> a{b/a{B/A}} ==> b *)
+(*CSC: la sostituzione ora e' implementata in maniera simultanea, ma *)
+(*CSC: dovrebbe diventare da sinistra verso destra: *)
+(*CSC: t{a=a/A;b/a} ==> \H:a=a.H{b/a} ==> \H:b=b.H *)
+(*CSC: per la roba che proviene da Coq questo non serve! *)
+let subst_vars exp_named_subst t =
+(*
+debug_print (lazy ("@@@POSSIBLE BUG: SUBSTITUTION IS NOT SIMULTANEOUS")) ;
+*)
+ let rec substaux k =
+ let module C = Cic in
+ function
+ C.Rel _ as t -> t
+ | C.Var (uri,exp_named_subst') ->
+ (try
+ let (_,arg) =
+ List.find
+ (function (varuri,_) -> UriManager.eq uri varuri) exp_named_subst
+ in
+ lift (k -1) arg
+ with
+ Not_found ->
+ let params =
+ let obj,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
+ (match obj with
+ C.Constant _ -> raise ReferenceToConstant
+ | C.Variable (_,_,_,params,_) -> params
+ | C.CurrentProof _ -> raise ReferenceToCurrentProof
+ | C.InductiveDefinition _ -> raise ReferenceToInductiveDefinition
+ )
+ in
+(*
+debug_print (lazy "\n\n---- BEGIN ") ;
+debug_print (lazy ("----params: " ^ String.concat " ; " (List.map UriManager.string_of_uri params))) ;
+debug_print (lazy ("----S(" ^ UriManager.string_of_uri uri ^ "): " ^ String.concat " ; " (List.map (function (uri,_) -> UriManager.string_of_uri uri) exp_named_subst))) ;
+debug_print (lazy ("----P: " ^ String.concat " ; " (List.map (function (uri,_) -> UriManager.string_of_uri uri) exp_named_subst'))) ;
+*)
+ let exp_named_subst'' =
+ substaux_in_exp_named_subst uri k exp_named_subst' params
+ in
+(*
+debug_print (lazy ("----D: " ^ String.concat " ; " (List.map (function (uri,_) -> UriManager.string_of_uri uri) exp_named_subst''))) ;
+debug_print (lazy "---- END\n\n ") ;
+*)
+ C.Var (uri,exp_named_subst'')
+ )
+ | C.Meta (i, l) ->
+ let l' =
+ List.map
+ (function
+ None -> None
+ | Some t -> Some (substaux k t)
+ ) l
+ in
+ C.Meta(i,l')
+ | C.Sort _ as t -> t
+ | C.Implicit _ as t -> t
+ | C.Cast (te,ty) -> C.Cast (substaux k te, substaux k ty)
+ | C.Prod (n,s,t) -> C.Prod (n, substaux k s, substaux (k + 1) t)
+ | C.Lambda (n,s,t) -> C.Lambda (n, substaux k s, substaux (k + 1) t)
+ | C.LetIn (n,s,ty,t) ->
+ C.LetIn (n, substaux k s, substaux k ty, substaux (k + 1) t)
+ | C.Appl (he::tl) ->
+ (* Invariant: no Appl applied to another Appl *)
+ let tl' = List.map (substaux k) tl in
+ begin
+ match substaux k he with
+ C.Appl l -> C.Appl (l@tl')
+ | _ as he' -> C.Appl (he'::tl')
+ end
+ | C.Appl _ -> assert false
+ | C.Const (uri,exp_named_subst') ->
+ let params =
+ let obj,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
+ (match obj with
+ C.Constant (_,_,_,params,_) -> params
+ | C.Variable _ -> raise ReferenceToVariable
+ | C.CurrentProof (_,_,_,_,params,_) -> params
+ | C.InductiveDefinition _ -> raise ReferenceToInductiveDefinition
+ )
+ in
+ let exp_named_subst'' =
+ substaux_in_exp_named_subst uri k exp_named_subst' params
+ in
+ C.Const (uri,exp_named_subst'')
+ | C.MutInd (uri,typeno,exp_named_subst') ->
+ let params =
+ let obj,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
+ (match obj with
+ C.Constant _ -> raise ReferenceToConstant
+ | C.Variable _ -> raise ReferenceToVariable
+ | C.CurrentProof _ -> raise ReferenceToCurrentProof
+ | C.InductiveDefinition (_,params,_,_) -> params
+ )
+ in
+ let exp_named_subst'' =
+ substaux_in_exp_named_subst uri k exp_named_subst' params
+ in
+ C.MutInd (uri,typeno,exp_named_subst'')
+ | C.MutConstruct (uri,typeno,consno,exp_named_subst') ->
+ let params =
+ let obj,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
+ (match obj with
+ C.Constant _ -> raise ReferenceToConstant
+ | C.Variable _ -> raise ReferenceToVariable
+ | C.CurrentProof _ -> raise ReferenceToCurrentProof
+ | C.InductiveDefinition (_,params,_,_) -> params
+ )
+ in
+ let exp_named_subst'' =
+ substaux_in_exp_named_subst uri k exp_named_subst' params
+ in
+ C.MutConstruct (uri,typeno,consno,exp_named_subst'')
+ | C.MutCase (sp,i,outt,t,pl) ->
+ C.MutCase (sp,i,substaux k outt, substaux k t,
+ List.map (substaux k) pl)
+ | C.Fix (i,fl) ->
+ let len = List.length fl in
+ let substitutedfl =
+ List.map
+ (fun (name,i,ty,bo) -> (name, i, substaux k ty, substaux (k+len) bo))
+ fl
+ in
+ C.Fix (i, substitutedfl)
+ | C.CoFix (i,fl) ->
+ let len = List.length fl in
+ let substitutedfl =
+ List.map
+ (fun (name,ty,bo) -> (name, substaux k ty, substaux (k+len) bo))
+ fl
+ in
+ C.CoFix (i, substitutedfl)
+ and substaux_in_exp_named_subst uri k exp_named_subst' params =
+(*CSC: invece di concatenare sarebbe meglio rispettare l'ordine dei params *)
+(*CSC: e' vero???? una veloce prova non sembra confermare la teoria *)
+ let rec filter_and_lift =
+ function
+ [] -> []
+ | (uri,t)::tl when
+ List.for_all
+ (function (uri',_) -> not (UriManager.eq uri uri')) exp_named_subst'
+ &&
+ List.mem uri params
+ ->
+ (uri,lift (k-1) t)::(filter_and_lift tl)
+ | _::tl -> filter_and_lift tl
+(*
+ | (uri,_)::tl ->
+debug_print (lazy ("---- SKIPPO " ^ UriManager.string_of_uri uri)) ;
+if List.for_all (function (uri',_) -> not (UriManager.eq uri uri'))
+exp_named_subst' then debug_print (lazy "---- OK1") ;
+debug_print (lazy ("++++ uri " ^ UriManager.string_of_uri uri ^ " not in " ^ String.concat " ; " (List.map UriManager.string_of_uri params))) ;
+if List.mem uri params then debug_print (lazy "---- OK2") ;
+ filter_and_lift tl
+*)
+ in
+ List.map (function (uri,t) -> (uri,substaux k t)) exp_named_subst' @
+ (filter_and_lift exp_named_subst)
+ in
+ if exp_named_subst = [] then t
+ else substaux 1 t
+;;
+
+(* subst_meta [t_1 ; ... ; t_n] t *)
+(* returns the term [t] where [Rel i] is substituted with [t_i] *)
+(* [t_i] is lifted as usual when it crosses an abstraction *)
+let subst_meta l t =
+ let module C = Cic in
+ if l = [] then t else
+ let rec aux k = function
+ C.Rel n as t ->
+ if n <= k then t else
+ (try
+ match List.nth l (n-k-1) with
+ None -> raise RelToHiddenHypothesis
+ | Some t -> lift k t
+ with
+ (Failure _) -> assert false
+ )
+ | C.Var (uri,exp_named_subst) ->
+ let exp_named_subst' =
+ List.map (function (uri,t) -> (uri,aux k t)) exp_named_subst
+ in
+ C.Var (uri,exp_named_subst')
+ | C.Meta (i,l) ->
+ let l' =
+ List.map
+ (function
+ None -> None
+ | Some t ->
+ try
+ Some (aux k t)
+ with
+ RelToHiddenHypothesis -> None
+ ) l
+ in
+ C.Meta(i,l')
+ | C.Sort _ as t -> t
+ | C.Implicit _ as t -> t
+ | C.Cast (te,ty) -> C.Cast (aux k te, aux k ty) (*CSC ??? *)
+ | C.Prod (n,s,t) -> C.Prod (n, aux k s, aux (k + 1) t)
+ | C.Lambda (n,s,t) -> C.Lambda (n, aux k s, aux (k + 1) t)
+ | C.LetIn (n,s,ty,t) -> C.LetIn (n, aux k s, aux k ty, aux (k + 1) t)
+ | C.Appl l -> C.Appl (List.map (aux k) l)
+ | C.Const (uri,exp_named_subst) ->
+ let exp_named_subst' =
+ List.map (function (uri,t) -> (uri,aux k t)) exp_named_subst
+ in
+ C.Const (uri,exp_named_subst')
+ | C.MutInd (uri,typeno,exp_named_subst) ->
+ let exp_named_subst' =
+ List.map (function (uri,t) -> (uri,aux k t)) exp_named_subst
+ in
+ C.MutInd (uri,typeno,exp_named_subst')
+ | C.MutConstruct (uri,typeno,consno,exp_named_subst) ->
+ let exp_named_subst' =
+ List.map (function (uri,t) -> (uri,aux k t)) exp_named_subst
+ in
+ C.MutConstruct (uri,typeno,consno,exp_named_subst')
+ | C.MutCase (sp,i,outt,t,pl) ->
+ C.MutCase (sp,i,aux k outt, aux k t, List.map (aux k) pl)
+ | C.Fix (i,fl) ->
+ let len = List.length fl in
+ let substitutedfl =
+ List.map
+ (fun (name,i,ty,bo) -> (name, i, aux k ty, aux (k+len) bo))
+ fl
+ in
+ C.Fix (i, substitutedfl)
+ | C.CoFix (i,fl) ->
+ let len = List.length fl in
+ let substitutedfl =
+ List.map
+ (fun (name,ty,bo) -> (name, aux k ty, aux (k+len) bo))
+ fl
+ in
+ C.CoFix (i, substitutedfl)
+ in
+ aux 0 t
+;;
+
+Deannotate.lift := lift;;
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